Ladder-type band-pass filters



Nav. 19, 1957 Filed May E, 1953 J. OSWALD LADDER-TYPE BAND-PASS FILTERS6 Sheets-Sheet 1 \L o U1 011 \"1 X UJ (df 0a HVEHTDR The@ us5 OswALDNov. 19, 1957 F110@ May 5. 1953 J. oswALD 2,814,021

LADDER-TYPE BAND-PASS FILTERS 6 Sheets-Sheet 2 mvEHToR: TMQUES OsamuNov. 19, 1957 l J. oswALD 2,814,021

LADDEmTYPE BAND- PASS FILTERS Filed May 5, 1953 S Sheets-Sheet 5 V 6@auf gaaf/502+@ aa/efe /M/ a (00,054? mvEHTDR IVAQQUES SMLD Nov. 19,1957 J. OSWALD LADDER-TYPE BAND-PASS FILTERS Filed May 5. 1953 6Sheets-Sheet 4 Nov. 19, l1957 J. OSWALD LADDR-TYPE BAND-PASS FILTERSFiled May 5. 1953 6 Sheets-Sheet 5 Nov. 19, 1957 J. OSWALD 2,814,021

LADDER-TYPE BAND-PASS FILTERS Fild May 5, 1953 6 Sheets-Sheet 6LADDER-TYPE BAND-PASS FILTERS Jacques Oswald, Paris, France, assigner toCompagnie arent IndustrielleV des Telephones, Paris, France, a corporaytion of France Application May 5, 1953, Serial N o. 353,142 Claimspriority, application France May 8, 1952 z Claims. (ci. assm The presentinvention relates to, new cells for laddertype band filters. It is wellknown that ladder-type filters can be obtained conveniently by arrangingin cascade elle* mentary filters, which are called cells or half-cellswhen they only have two arms.

The possibility of putting these elementary filters in cascade dependson the identity of the image impedances of the quadripoles which arebeing connected; in these conditions the attenuations on images of thecomponent quadripoles are purely and simplyadded. The majority ofsemi-cells characteristic of band filters are well known and havealready been described long before this. However, there arecertainthree-branch cells, form a T or 1r, which cannot be reducedto'combinations of simple semicells and which are the object ofthepresent invention.

First of all it is necessary'to define the characteristic functions ofladder-type band filters and to indicate the corresponding notations.

will designate the image transfer exponent of a band filter. If theimage attenuation, that is, the real portion of 0, becomes infinite fora single frequencyf--real or complex-it can beshown that 0 satisfies arelation of the type:

in which p is the complex pulsation jw,yt v 1, `w1 the IOWer and UPP-@t.Cui-.0.1i fantasies., mp the. quantity and m a constant characteristicparameter of the peak of infinite attenuation. We will then take theexponent |1f:

w1 and infinity; we shall thenflrave a Ifunction which will 2,814,0ZlPatented- Nov. 19,4 1957 2 beV said to be of the type lM'; finally withthe same expression of 0; but in which l m= m0 the point of infiniteattenuation is shifted to infinity-it will be said that the function isof the class 1K.

By suitably combining two functions of attenuation of the firstV order,we get a function of Vattenuation of the second order, which has twopoints of attenuation, and will have an expression of the form:

@2i-1.2 (2) p2+w .2 p2+w.a

in which m is a characteristic parameter, and wa a frequency between w 1and w1, that is, in the pass band. The sign lcorresponds to thecombination of two functions of the saine type, lar or 1*,Athe signtothe combination of two functions of different types. According toA thepositions of the frequencies of infinite attenuation, the functions ofattenuation of the second order will be designated by 2M2, 2K2,` 2M'2,ZKZ, ZKM,V ZMK, ZMM', Z'MK, ZKM', ZKK'. For the five first functions theexponent +1 musst be chosen:l (2a) m(p2+wa2) V (P2-H0412) (P2-F011?) m`and wa having suitablevalues which will not be specified at the moment.For the live last p onent (-1) must be taken:

will now pass on (Wien:

'bf b* Vareimpedances of the second order. The impedances of thefourthorder are of the form:

Wwt were 1' (fair-@Wound vouw-lanzas) inwhich A aan?.

No. being a frequency in the upper attenuated band, w., a.

` 4frequency inthe lowrlattenuated band. VAccording to whether the value|1 or -1 were chosen for the exponent we have the `types of impedancesUd` or 4d-" Fig'. 1 represents the impedances'b, b*, d, d*, the zeroes ofthe image impedance being designated by a small circle,

' Athe poles by a cross and the branching points by a V.

- the frequency of infinite attenuation is situated between Fig. 2arepresents a T semi-cell' consisting of the simplest filter (ZKKbbt),hereinafter called a classic cell.

Fig.' 2b represents a T semicelltZMMbid)'called a derivative in MM" ofthe preceding semi-cell `shown in "the Afourth order d.

4functions the ex- Figs. 4a, 4b and 4c show three simple classicalsemicells having degenerate impedances.

Figs. 5a and 5b respectively represent an elementary filter embodyingthe principles of the present invention and having the impedancevariation (2MK/Cn*d) and its inverse.

Fig. 5a is an electrical schematic diagram of the filter incorporatingthe principles of the present invention and utilizing piezo-electricresonators.

Fig. 6a represents the elementary filter (2KM'/Cm*d) and Fig. 6brepresents its inverse.

Fig. 7 is a table giving the values of the elements of the filtersillustrated in Figs. 5a and 5b.

Fig. 7a is a table of notations showing the values of the symbols usedin Fig. 7.

Fig. 8 is a table giving the values of the elements of the filtersillustratedin Figs. Ga'and 6b.

Fig. 8a is a table of notations showing the values of the symbols usedin Fig. 8.

The filter section of Fig. 2b has ahorizontal branch consisting of aresonant circuit having the impedance variation illustrated in b* ofFig. 1. VThis horizontal branch is formed by the elements L1 and C1. Thevertical branch is formed with two resonant circuits in sists of theelements L2, C2 and Lz, C'z.

The filter network illustrated in Fig. 2c includes a vertical branchconsisting of an anti-resonant circuit L1 and C1 having the impedancevariation illustrated in b of Fig. l and a horizontal branch consistingof two antiresonant circuits in series formed by the elements L1', C1'and Lz', C2'. The horizontal branch has the impedance variationillustrated in d* of Fig. l.

VIf we refer to Fig. l, however, it will be seen that the impedances ofthe fourth order d, d* may show cases of degeneration. These arethe'cases in which the frequen-n cies wa, wa are merged with thefrontiers (0, w 1, w1 w). An index (i) will designate the degenerationsuch that wa or wa' becomes merged with the frequency w1. Furthermore,the letter chosen to represent the impedance is characteristic of thedegree of this impedance (degree of the rational fraction W2 consideredas function of e2).

For example, C., designates the impedance of the third order obtainedfrom the impedance of the fourth order d, when the frequency wa' tendsto infinity; C1 designates the impedance obtained from d when w.. ismerged with w 1; b1, represents the impedance uniting these characters.

Referring now to Fig. 3 the impedances of the second and third orderobtained by degeneration of the impedance of the fourth order d arerepresented.

vTheir expression is as follows:

g aLl-w12 bo'l/W-wrv 1324-61-12 wet-w02 p2+w 12 p2+w12) The impedancesbof", Cf?, C ll, etc. are obtained by substituting W*l for W (thusb0,1l=b 1,

Fig. 4 shows three simple classical semi-cells having degenerateimpedances. With the notations used, Fig. 4a

ll l d l para e an con represents the filter 1K/bo1*b) which is aT'semi-cell having a capacity Co in the horizontal branch thereof and ananti-resonant circuit (L1, C1) inits vertical branch, Fig. 4b the filter(1M/bo,1* Cm) which is a `T semi-cell 75 filters.

having a capacity Co in its horizontal branch with an impedancevariation illustrated in bm* and a vertical branch comprising a resonantcircuit'L1, C1 in parallel with a capacitor C1' or the equivalentpiezo-electric resonator and Fig. 4c the filter (lM'/Co* bo1*) having avertical branch with a capacity Cu with the impedance variationillustrated in boi* and a horizontal branch consisting of a capacitorC1' in series with an anti-resonant circuit (L1, C1).

If any two impedances W1, W2, are chosen from the impedances of thefirst and second order (degenerate or not) it can be proved that thereis always an infinity of filters of which the image impedances are W1,W2. Among all these filters there is one of which the class ofattenuation is lower in degree than all the others. A filter of thiskind will be termed e1ementary- The classical semi-cells of theband-filters are elementary For certain associations of impedances theelementary filter is formed of two semi-cells of a simpler type; forexample, the elementary impedance filter W1=bo,1*, W2=C1 is of class 2;it is the filter on the other hand.

It'will be noted that the structures of the second line are obtainedfrom those of the first by substituting 1/ p for p in its componentelements.

As, moreover, the passage from a T (or 1r) cell to a 1r (or T) cellinverse to the foregoing by substitution of inverse branches in thesecond structure, is well known, it will be sufficient to show that, forexample, the T-type cell: (2MK/Co*d) cannot be decomposed into matchedsemi-cells.

The decomposition of said cell would require, in effect, the use ofsemi-cells:

1K'/C0*W2,lM/W2 1K2/dW2,lM/Co*W2 W2 designating a common imageimpedance.

It is, however, easy to see that there is no semi-cell of the types:

1K'/Co*,1K'/d Type 1K'/Cu* mem-awww 112+@ 7 W1 C-l upfpZ-lewaf) qPLI-wa* The vertical branch should have as impedance:

Co*1 (P2lw12)(p+w1) 92-1 P(w12 w-12)(P2+wa'2) which is impossible byreason of the position of the zeros and the poles. Type 1K'/d ff(PiaLw-llziu). p (1324-02-12) (P2-fm2) which again is impossible owingto the non-alternation of the poles and the zeros.

lt will be remembered that the knowledge of the imageimpedance functionsW1, W2 and of the attenuation function q determines in an unique mannerthe branches of the corresponding T (or 1r) type cell, if such there be.

It is known, in effect, for example, that if W1, W2 and q respectivelyrepresent the image impedances and the attenuation function of a T-typereactive cell, and if W is the geometrical mean of the impedances;

the vertical branch of the T has as a reactance: WVq21 andthe horizontalbranches respectively have as reactances Wrq-WVq2-1, Wzq-Wi/qZ-l Thethree branches of the T-structure are therefore defined and can beobtained by the known methods of constructing reactances.

Referring to Fig. 5, the filter a has a point of infinite attenuationfor the frequency of resonance wa of the resonant circuits LzCz and LsCsand a point of attenuation at the infinite frequency. Its impedanceregarded from the left side is the impedance Co* of the classic cell ofFig. 4c, its impedance regarded from the right-hand side that of theclassic cell of Fig. 2b. Table No. l gives the exact value of theelements of this filter in the left hand column. The right hand columngives the value of the elements of the cell illustrated in Fig. 5b(2MK/Cod*), and which is obtained by replacing each of the impedances inthe left hand column by its inverse and multiplying by R2.

Figure 5a represents the same type of filter as in Figure 5a withpiezo-electric resonators substituted for some of the inductive andcapacitive elements of the filter. The piezo-electric resonator K1 isarranged in the series branch while the piezo-electric resonator K2 isarranged in the diagonal branch. The dotted lines and capacitorsrespectively :connected in parallel with the piezo-electric resonatorsK1 and K2 represent shunt capacitors 'y1 and 'y2 which may be connectedin parallel if desired.

Fig. 6a represents the elementary filter (2KM/C *11), Fig. 6b itsinverse. Filter 6b for example has a point of infinite attenuation atzero frequency, another at the frequency wu' of anti-resonance of thestopper circuits L2C2 and LaCs.

The impedance regarded from the left is the impedance C of the lter ofFig. 4b, and that seen from the right is the impedance d* of the filterof Fig. 2c.

Table No. 2 gives the exact value of the elements of this filter in theleft hand column. The right hand column gives the elements of the cellillustrated in Fig. 6b.

All these filters, which cannot be obtained by simple combination ofknown cells, have the remarkable property of having on one side anundegenerate impedance of the fourth order with a more simpletermination than the classic semi-cells of Figs. 2b and 2c. In effectthe terminal impedance (d) of the filter of Fig. 5a is a seriesresonantcircuit LaCs, while that of the filter of Fig. 2b comprises two resonantcircuits in parallel.

Another property of the filters of Figs. 5a and 6 is that of beingdirectly connected to the cells of Figs. 4c and 4b, which are much usedbecause they are economical.

On the other hand the classic cells of Figs. 2b and 2c are onlyconnected to cells having an impedance of the second order. Finally, thestructures of Figs. 5a and 6b, which only comprise three inductances,are particularly to be recommended when the price of the capacities isclearly lower than that of the inductances. They can provideterminations having a regular impedance, and on the other hand can beinterconnected to form a composite lter having a regular input impedanceand a high degree of attenuation.

Moreover the cells 2MK/c*d and 2KM'/cd* each have two arms formed byplacing a stopper circuit and a capacity in series (equivalent toplacing a resonant circuit and a capacity in parallel).

It is known that these structures can, in certain cases be obtained by apiezo-electric crystal (for example of quartz) possibly completed by acapacity.

The present invention provides for the use in filters with relativelynarrow band, of the cells 2MK/c*d and 2KM'/cd*, each produced by meansof two piezo-electric resonators and an ordinary stopper circuit (or aresonant circuit) for the third arm of the cell.

This form is possible, because the orders of magnitude of the variouselements for a rather high nominal impedance and a relative band widthnot exceeding a few hundredths are quite suitable--which is not alwaysthe case with the known types of ladder-type semi-cells.

What is claimed is: K

l. An asymmetrical T-type filter cell with a single pass band limited bya lower cut-olf frequency f 1 and a higher cut-off frequency f1,comprising a horizontal branch including a resonant circuit having aresonance frequency fm lower than L1; a vertical branch including acapacitor in parallel with a resonant circuit having the same resonancefrequency fw; a second horizontal branch including a capacitor in serieswith an anti-resonant circuit tuned to ia frequency f higher than f1said filter cell having 'the following: (a) an image transfer constant 0so that coth20 is a rational fraction of the second degree in p3, pstanding for the quantity 21rif, where f is the frequency of the currentapplied to the cell, said fraction having a value equal to 1 when thesaid frequency f becomes infinite, and also when f has the value fm; (b)an image impedance which when squared is a rational fraction in thefourth degree in p2, the said fraction having an infinite value when thefrequency f has one of the following values: O, f 1, f1, and having azero value when the frequency is equal to for to f; (c) a second imageimpedance which when squared is a rational fraction in the third degreein p2, the said fraction having an infinite value when the frequency fis equal to 0 or fw', and having a zero value when the frequency fbecomes equal to f 1 or to f1.

2. A cell in accordance with claim l having a relatively narrow passband and a high impedance, including piezoelectric resonators in two ofits branches and a resonant circuit in the third branch.

References Cited in the file of this patent UNITED STATES PATENTS1,795,204 Espenshied Mar. 3, 1931 2,591,838 Leroy Apr. 8, 1952 2,619,535Prior et al Nov. 25, 1952 2,762,018 Purington Sept. 4, 1956

